Row guidance parameterization with hough transform

ABSTRACT

Systems and techniques for row guidance parameterization with Hough transform are described herein. An electronic representation of a field (ERF) can be received. The ERF can include a set of feature sets including one of a set of crop row features or a set of furrow features. A first parameter space can be produced by applying a slope-intercept Hough transform (SLIHT) to members of a feature set. Peaks in the first parameter space can be identified. A second parameter space can be produced by application of the SLIHT to the peaks. A vanishing point can be calculated based on a vanishing point peak in the second parameter space. A track-angle error can be calculated from the vanishing point.

BACKGROUND

Many crops that are farmed are row crops. Row crops are arranged intorows that are generally equally spaced parallel rows in a fieldseparated by furrows. Tending row crops generally involves passingagricultural equipment (AEQ) (e.g., tractors, planters, harvesters,irrigators, fertilizers, etc.) over the field. Generally, the AEQ shouldfollow the rows such that support structures (e.g., wheels, treads,skids, etc.) remain in the furrows so as not to damage the crops.Further, equipment dealing directly with the crops should follow thecenterline of the crop rows.

Navigation systems using an external location mechanism have beenemployed to facilitate automatic navigation of AEQ. These systemsinclude using global position system (GPS) units to locate the positionof AEQ with respect to crop rows. Generally, these systems use aninitialization operation to determine positions through which the AEQshould pass and then provide information about the current position ofAEQ in a field in order to facilitate navigation. An exampleinitialization operation can include using a GPS unit to record themovement of AEQ as the row crops are planted. This recording can laterbe used to guide the AEQ for subsequent operations.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings, which are not necessarily drawn to scale, like numeralsmay describe similar components in different views. Like numerals havingdifferent letter suffixes may represent different instances of similarcomponents. The drawings illustrate generally, by way of example, butnot by way of limitation, various embodiments discussed in the presentdocument.

FIG. 1 illustrates an example of a system for row guidanceparameterization with Hough transform, according to an embodiment.

FIGS. 2A and 2B illustrate two perspectives of a vehicle in a field androw guidance parameters, according to an embodiment.

FIG. 3 illustrates an example of an electronic representation of a fieldused for row guidance parameterization with Hough transform, accordingto an embodiment.

FIG. 4 illustrates an example of a Hough transform parameter space forcrop rows, according to an embodiment.

FIG. 5 illustrates an example of determined crop row lines superimposedon an electronic representation of a field, according to an embodiment.

FIG. 6 illustrates an example of a Hough transform parameter space forfurrows, according to an embodiment.

FIG. 7 illustrates an example of determined furrow lines superimposed onan electronic representation of a field, according to an embodiment.

FIG. 8 illustrates an example of a Hough transform parameter space ofthe Hough transform spaces for crops and furrows, according to anembodiment.

FIG. 9 illustrates an example of determined crop row lines, furrowlines, and vanishing point superimposed on an electronic representationof a field, according to an embodiment.

FIG. 10 illustrates an example of cross-track distance normalization,according to an embodiment.

FIG. 11 illustrates an example of a method for row guidanceparameterization with Hough transform, according to an embodiment.

FIG. 12 illustrates an example of a method for determining a cross-trackdistance, according to an embodiment.

FIG. 13 is a block diagram illustrating an example of a machine uponwhich one or more embodiments can be implemented.

DETAILED DESCRIPTION

Although modern GPS navigation can be highly accurate, it requires theinitialization operation to have been performed. In cases where the rowlocations were not recorded at planting, or where this data isunavailable (e.g., lost or corrupted), the initialization operationneeds to be performed (e.g., again or for the first time) prior to usingGPS. Traditionally, the initialization operation has been performed by ahuman operator controlling the AEQ and recording positioning data. Usinga human operator to guide the AEQ can be a tedious job requiring askilled operator; all factors that can lead to errors and higher costs.

Computer vision (CV) can be used to guide AEQ down the crop rows. A CVnavigation system generally involves a sensor, such as a camera, mountedon the AEQ to collect features (e.g., of the crop rows or furrows) ofthe environment. These features can be used to ascertain AEQ positionrelative to row or furrow positions and provide that information asparameters to a steering module to control the AEQ. One problem that canarise is a zigzag effect where the AEQ moves towards the target row andpasses over it only to turn back towards the row and pass over it again.This situation occurs because the angle at which the AEQ approaches thetarget row is not considered in the steering calculations. Another issuethat can arise in CV navigation systems can include selecting anotherrow as a target row when the current target row is interrupted (e.g., isbroken or not continuous to the sensor at a given point).

Determining two guidance parameters can address the previously mentionedproblems with CV navigation systems: track-angle error (TKE) andcross-track distance (XTK). TKE involves the angle between the forwarddirection of the AEQ and the rows such that, when the AEQ is followingthe rows, the TKE is 0°, and when the AEQ is moving perpendicular to therows, the TKE is 90°. Accordingly, the TKE can be considered the currentangle-of-attack for AEQ moving towards a given row. The CV navigationsystem sensor data causes the generally parallel crop rows or furrows toappear to converge at a vanishing point on the horizon. This vanishingpoint can be used with the current orientation of the AEQ to determinethe TKE.

A slope-intercept Hough transform (SLIHT) can be used to determine thevanishing point from crop row or furrow features captured by the sensor.The original Hough transform uses a parameter space with a slope of aline on one axis and an intercept of a line in a second axis where aline is expressed as y=mx+b, where m is the slope and b is the xintercept of the line in a Cartesian coordinate system. For example,each image pixel whose color matches that of the straight lines sought,may lie on any of a number of possible lines represented in theparameter space by their slope and intercept parameters. These lines maybe identified by computing for each possible intercept value in theparameter space of the slope of a line from that intercept to the pixelunder consideration. Additionally, or alternatively, for each possibleslope value, the value may be computed at which a line of that slopewould intercept the image axis. For example, slope parameters in theparameter space can be used in conjunction with the pixel to determinecorresponding intercept parameters in the parameter space. For each suchline, the value of that line in the parameter space is incremented.Thus, pixels from the image can contribute to numerous parameter spacepositions (e.g., a single pixel can cause several parameter spacecoordinates to be incremented). However, when several pixels fall on aline in the image, the corresponding parameter space position for thatline is incremented for each of those pixels. Accordingly, thatparameter space position will have a higher value than other parameterspace positions that represent lines that are not found in the image.

Once all the image pixels of the color sought have contributed to theparameter-space accumulation, the parameter space can be analyzed todetermine lines that are represented by the pixels in the image. Theselines appear as peaks (points with high incrementation relative to otherpoints) in the parameter space due to the cumulative effect of beingincremented for each pixel lying on the line. One problem with theoriginal Hough transform originates with the rise in unbounded parametervalues in assessing vertical lines, as found when following crop rows.One solution to this problem is to use polar coordinates as parameters.Using polar coordinates, however, introduces greater computationalcomplexity and thus cost. Instead, the original Hough transform can bemodified to address the vertical line issue presented in following croprows by reformulating the parameters from

$\frac{y}{x}$

and a y intercept to a slope of

$\frac{x}{y}$

and an x intercept; i.e., the lines defined by the parameter space arein the form of x=my+b. As used herein, this modification to the originalHough transform is referred to as a vertical SLIHT, and the originalHough transform is referred to as a horizontal SLIHT. Alternatively, thesensor image of the crop rows or furrows can be rotated (e.g., 90°) toreduce the vertical nature of lines corresponding to the crop rows orfurrows and allow the original Hough transform to be used. As usedherein, any Hough transform where the parameters are slope and interceptis SLIHT.

After applying the SLIHT to the sensor image, lines representing croprows or furrows can be determined by analyzing the sensor image. In anexample, the vanishing point can be determined by determining theintercept of two or more of these lines. In an example, the vanishingpoint can be determined by cascading the SLIHT. In the first parameterspace, the peaks representing the converging lines fall on a linethemselves in that parameter space. By applying the SLIHT to the firstparameter space to produce a second parameter space (known as cascadingthe SLIHT), a convergence peak in the second parameter space willrepresent that line. The coordinates of the convergence peak are thecoordinates of the vanishing point in the original sensor image with they parameter negated. Thus, the vanishing point can be determined bycascading the SLIHT. The determined vanishing point can provide the TKEbecause the horizontal displacement of the vanishing point isproportional to the tangent of the TKE. In an example, the vanishingpoint can be used to determine the horizon in order to adjust for errorsintroduced by the particular perspective of the sensor.

The XTK is the distance between the current position of the AEQ and thetarget row or furrow. Generally, the target row or furrow is that whichis closest to the AEQ, although another may be selected. Because thecrop rows are generally spaced an equal distance from each other,distances between multiple lines representing the crop rows or furrowscan be used to increase accuracy by reducing errors in a given distancemeasurement. For example, a distance between each pair of peaks can bedetermined, such as between peaks 1 and 2, 1 and 3, 1 and 4, 2 and 3, 2and 4, and 3 and 4. These determined differences can be ordered based ontheir values. The smallest distance can be considered the spacingbetween rows or furrows. The largest spacing can be divided by thesmallest spacing to determine the number of rows or furrows the largestdetermined difference encompasses. In an example, the result of thedivision can be rounded to the nearest integer to reflect the number ofrows or furrows. The largest determined difference can be divided by thenumber of rows or furrows that it encompasses. Thus, error in themeasurement of the peaks can be diffused among several row or furrowcalculations, reducing its impact. In an example, only those peaks thatfall on (within a threshold) the line represented by the convergencepeak are considered in the XTK calculation. In an example, a resultingsingle crop-row-spacing value is approximately equal to the furrowspacing.

Once this calculation of the crop-row spacing in units of interceptpixels is complete, the differences in distance between a line from theAEQ to the vanishing point, representing a line on the field parallel tothe crop rows, and the intercepts of crop rows or furrows, modulo thecrop-row spacing, can be used to determine the XTK in units of thespacing in intercept pixels, then scaled to the known spacing of theactual crop rows. In an example, a peak can be added in the firstparameter space at a point on the line represented by the vanishingpoint peak, between other peaks at the previously determined crop-rowspacing, in order to infer the target crop row position when it isinterrupted. In another example, the residuals of the intercept spacingof crop rows or furrow lines (first parameter space peaks) in the sensorimage, modulo the crop-row spacing, may be averaged in various ways toincrease accuracy and to infer the target crop-row position when it isinterrupted.

Using TKE and XTK as parameters to the steering module can allow for aneffective row guidance system of AEQ using CV. Thus, costs and error canbe reduced in performing an initialization operation for GPS basedsystems, or for automatic navigation of AEQ when GPS, or othernavigation systems, are unavailable. Additional details and examples areprovided below.

FIG. 1 illustrates an example of a system 100 for row guidanceparameterization using SLIHT. The system 100 can include a scene module105, a transform module 110, a track-angle error module 115 and across-track distance module 120. In an example, the system 100 can beaffixed to AEQ and arranged to facilitate CV navigation of the AEQ.

The scene module 105 can be arranged to receive an electronicrepresentation of a field (ERF). The ERF can include any electronicrepresentation of the field, including, a digital image (raw orcompressed), a vector image, a collection of distance data (e.g., fromlaser range-finding, radar, etc.) translated into a digital image, orcombinations of these (e.g., a plurality of raster images from multiplesources and distance data). In an example, the ERF can be captured by asensor module 125 to which the scene module 105 is arranged tocommunicate. In an example, the sensor module 125 can include, or cancontrol, a plurality of sensors. In an example, the plurality of sensorsincludes a digital camera (e.g., video or still). In an example, adigital camera can include a filter to at least one of color bias thecaptured image, increase color contrast in the captured image, or reduceinformation (e.g., blur) in the captured image. An example of colorbiasing the captured image is that of a green crop planted in red-tintedsoil. A red-filter can be applied to a first sensor arranged to capturean image of the crops or a green filter can be applied to a secondsensor to capture an image of the furrows. Modifying the captured imageat the sensor can provide a cost-effective way to facilitate reducedprocessing or errors when using SLIHT, as discussed below.

The ERF can include a set of feature sets. A feature set is a set ofelements that can be distinguished from the ERF and represent somethingin the ERF. For example, a set of crop row features can include pixels,lines, other geometric shapes, colors, etc. from the ERF that represent(e.g., correspond to) crop rows in the ERF. In an example, the set offeature sets can include a set of crop row features. In an example, theset of feature sets can include a set of furrow features.

In an example, the scene module 105 can be arranged to receive a digitalimage of the field (e.g., from the sensor module 125) and apply atransform to the digital image to produce the ERF. Because SLIHToperates on pixels in the ERF, modifying the original source sensor datacan increase accuracy and efficiency. Accordingly, reducing the numberof pixels, or providing greater clarity as to which pixels apply to croprows or furrows, can facilitate SLIHT.

In an example, the transform can include color modeling. As used herein,color modeling is the manipulation of color information from the sensorinput to a model output. The model output can be arranged to permiteasier processing of various techniques described herein, such as SLIHT.For example, given green crops planted in brown soil, the colors of thesource digital image can be processed, for example, to increase thecontrast between these two features to better tell them apart. In anexample, adjustments can be made to address different lighting effects(e.g., lighting source color temperature or shadows) such that, forexample, shadowed crops can be recognized in the same manner asunshadowed crops.

In an example, color modeling can include color normalization. Colornormalization can include compensating for illumination variations(e.g., from shadows due to clouds, buildings, AEQ, etc.) in the inputinformation (e.g., removing brightness information from un-normalizedpixels without altering the hue). In an example, in three dimensions,color normalization can include finding an intersection of color vectorextensions having non-negative components and a surface (e.g., sphere,cube, plane, etc.). For example, a pixel's color can be represented as aCartesian vector comprising non-negative components emphasizing variouswavelengths. The wavelengths can include, but are not limited to, red,green, and blue components of visible light, infrared light, andultraviolet light. In an example, one or more of the color vectors canbe divided by the root-sum-square of their respective components. Inthis result, the color vectors are normalized to an octant of a sphere.In an example, the one or more color vectors can be divided by theirrespective largest components. In this result, the one or more colorvectors are normalized to a cube with one corner at the origin and sidesaligned with the color-component axes. In an example, the one or morecolor vectors can be divided by the sum of their respective components.In this result, the one or more color vectors are normalized to anequilateral triangular segment of a plane with its corners symmetricallylocated on the color component axes. In an example, the describednormalizations can include projection of a normalized multi-dimensionalcolor vector into a space of one fewer dimensions. For example, thedescribed normalizations in three or more dimensions can include atwo-dimension projection.

As previously described, the color modeling can also include resolvingthe colors in the source digital image to produce the ERF. For example,given the green crop, the colors that are not green can be reduced oreliminated and the contrast between the green and other colors can beincreased. In an example, the color resolving can include usingnormalized color component vectors (e.g., as described above). In anexample, the color resolving can include calculating the respective dotproduct of a normalized color vector with a respective radius vector ofa point on the periphery of the normalization surface (e.g., sphere,cube, plane, etc.) In an example, the dot product can be compared with athreshold value to determine if it is either a target color or not. Inan example, with two feature sets, thresholding can be performed on onefeature set (e.g., crop rows) to determine pixels pertinent to thatfeature set. Pixels pertinent to the second feature set can bedetermined by simply taking the complement to the results of the firstfeature set thresholding. In an example, the color vectors can beconverted to a single bit representing a pixel by the thresholding. Thethreshold can be one of an average, median, minimum, maximum, or othervalue of the resolved color component represented by the color vectors.

In an example, the color resolving can include mapping the color vectorsto a sphere where saturated colors are at the equator and white is atthe north pole (e.g., centered on a z-axis of the Cartesian colorspace). Three-dimensional color vectors from the center of the spherecan be used to ascertain pixel color values in the ERF to exaggeratecontrast between the colors. In an example, the color resolving caninclude projecting the color cube surfaces—created using the colordimension projections onto the color cube—isometrically to a regularhexagon and then onto a hemisphere circumscribing the hexagon, where thehemisphere's center is at the plane of the hexagon and forms the originof the projected color vectors of uniform magnitude.

In an example, the results of the color modeling (e.g., color vectorsresulting from one or more of the color normalization or the colorresolving) can be used to create one or more digital images comprisingthe ERF. In an example, individual digital images can be created foreach color, so as to produce an image for the green crop and anotherimage for the brown furrows. Other colors can be resolved for anyfeature set being considered. For example, instead of green, orange,pink, yellow, red, etc., can be resolved to identify a variety of crops.Further, in the case of distinctive soil (or other furrow material)colors, the distinctive color can be resolved. In this example, thecollection of digital images comprise the ERF.

In an example, the transform can include downsampling the digital image.Downsampling can include reducing the resolution of the source image byapplying one or more downsampling operations. In an example, thedownsampling operations can use the information from a plurality ofpixels to determine the value of a single downsampled pixel. In anexample, the plurality of pixels can be determined by their inclusion ina pixel mask applied to the source image and corresponding to thedownsampled pixel. For example, four pixels arranged in a square in thesource image can be combined to determine the value of the downsampledpixel centered in the square. In an example, the combination of thesource image pixels can include summing the source pixels. In anexample, the combination can include averaging the source pixels. In anexample, the result of the combination can be thresholded to determinethe final value of the downsampled pixel.

In an example, the downsampling operations can include distortioncorrection. For example, a circularly symmetric lens of a camera canproduce a circular distortion, centered in the source image, that causesa bowing effect known as a barrel distortion. This can be problematicwhen trying to determine positions for essentially straight crop rows orfurrows. In an example, the distortion correction can correct the lensdistortion. In an example, the distortion correction can choose sourceimage pixels in such a way as to correct the distortion in thedownsampled image. For example, independent multiplication of sourcepixel coordinates can be performed by an even function of the pixel'sradial distance from the center of the source image to determine thedownsampled pixel that will use the source pixel value. This correctsthe barrel distortion without using a square-root, because aneven-polynomial function approximation is equivalent to a polynomial inthe square of radial distance, which is the sum of the squares of thepixel coordinates.

In an example, the transform can include removing members of a featureset. As noted above, pixels in the source image are features in afeature set. For example, green pixels can be features in the featureset of crop rows where the crop is green. Also, as discussed previously,the SLIHT is performed using these features. Accordingly, reducing thenumber of features in a feature set can reduce computational complexityand thus reduce costs or increase performance of the system 100. In anexample, the relevant lines are centered on one of crop rows or furrows.Accordingly, data not relevant to the center of these features can beremoved. In an example, removing members of the feature set includesidentifying pixels on a color transition border and removing them fromthe feature set. For example, a green pixel next to a brown pixel (orblank pixel after removal) can be removed from the feature set. In anexample, the removal is performed when the pixel has a neighbor of thesame value and prevented otherwise. For example, a brown pixel with agreen pixel to its left and a brown pixel to its right can be removed.However, a brown pixel with a blank pixel to both its right and leftcannot be removed. This can prevent removal of pixels used to determinethe center of a feature. In an example, the removal neighbor isdetermined in a particular direction. In an example, the particulardirection is parallel to the intercept axis in the parameter space. Inan example, the particular direction is horizontal.

The transform module 110 can be arranged to produce a first parameterspace by performing a SLIHT on members of a feature set in the set offeature sets. The first parameter space includes a first slope parameterand a first intercept parameter. Producing the first parameter spaceusing SLIHT is described above. An example of the first parameter spaceis illustrated in FIG. 4 and described below. In producing the firstparameter space, a vertical SLIHT can be used when the orientation ofthe ERF is such that the crop rows or furrows are generally parallel tothe direction of the perspective represented in the ERF. In an example,a horizontal SLIHT can be used by rotating the ERF 90°. Unless otherwisestated, further examples refer to vertical SLIHT; however these examplesare generally applicable to horizontal SLIHT with SLIHT modifications.

The transform module 110 can also be arranged to identify peaks in thefirst parameter space. As previously described, parameter space peaksrepresent lines in the ERF. For example, if the crop row features areused, peaks in the first parameter space represent lines of crop rows inthe ERF. As described below, FIGS. 4 and 5 illustrate this relationship.Often, the first parameter space includes many values (e.g., buckets,pixels, etc.) of varying nature. That is, given a feature setrepresenting a wide crop row, more than one line of similar parameterscan fall within the feature. This produces clusters of parameter spacevalues. In an example, to determine a peak, parameter space values aremodified based on a threshold. For example, if the value is below athreshold, it is zeroed, or if it is above the threshold, it ismaximized. In an example, values above a threshold are grouped, and ageometric center of the group is used to identify the peak.

The transform module 110 can be arranged to produce a second parameterspace by performing the SLIHT on the peaks. That is, SLIHT is performedon the first parameter space using the peaks as input. Because the croprows and furrows converge to a vanishing point, the peaks in the firstparameter space fall on a line within that parameter space. Thus, thesecond parameter space includes a peak representing this line. This peakis a vanishing point peak that can be used to calculate the vanishingpoint in the ERF.

Adding more data points can increase the accuracy of calculating thevanishing point peak location using the second SLIHT. The additionaldata points can come from a second feature set. For example, if thefirst parameter space was derived from a crop row feature set, a furrowfeature set can be used to derive a third parameter space with peaksthat can also be used in the second SLIHT to produce the secondparameter space. In an example, to produce the second parameter space,the transform module 110 can be arranged to produce the third parameterspace by performing the SLIHT on members of a second feature set in theset of feature sets. In this example, the feature set and the secondfeature set are different members of the set of feature sets, such asthe crop row feature set and the furrow feature set. FIGS. 6 and 7illustrate the production of the third parameter space and correspondinglines in the ERF. The transform module 110 can be arranged to identifysecond peaks in the third parameter space and to adjust the secondparameter space with the output of performing SLIHT on the second peaks.Additional feature sets can be used while they represent lines thatintersect at the vanishing point. In an example, different feature setscan have different priorities such that they are processed first, or aregiven greater weight in the second SLIHT calculation.

The track-angle error module 115 can be arranged to calculate thevanishing point based on the vanishing point peak in the secondparameter space. As previously discussed, the vanishing point in the ERFcan be determined by the vanishing point peak. In fact, the x componentof the vanishing point peak in the second parameter space is the xcomponent of the vanishing point in the ERF and the y component of thevanishing point peak is the negated y component of the vanishing pointin the ERF. The following illustrates the relationship between thevanishing point peak and the vanishing point in the ERF:

-   -   The SLIHT H(p,q) of a line passing through points p and q in the        ERF is:

${H\left( {p,q} \right)}_{y} = \frac{q_{x} - p_{x}}{q_{y} - p_{y}}$H(p, q)_(x) = p_(x) − p_(y ) ⋅ H(p, q)_(y) = q_(x) − q_(y) ⋅ H(p, q)_(y)

-   -   To find the vanishing point in the ERF, two different crop rows        (or furrows) can be characterized by their x intercepts, p and        q, and the vanishing point v, resulting in:

H(p, v)_(x) = p_(x)${H\left( {p,v} \right)}_{y} = \frac{v_{x} - p_{x}}{v_{y}}$H(q, v)_(x) = q_(x)${H\left( {q,v} \right)}_{y} = \frac{v_{x} - q_{x}}{v_{y}}$

-   -   The cascaded SLIHT, H(H(p, v), H(q, v)), of the line passing        through these points is:

${H\left( {{H\left( {p,v} \right)},{H\left( {q,v} \right)}} \right)}_{y} = {\frac{q_{x} - p_{x}}{\frac{v_{x} - q_{x}}{v_{y}} - \frac{v_{x} - p_{x}}{v_{y}}} = {- v_{y}}}$$\begin{matrix}{{H\left( {{H\left( {p,v} \right)},{H\left( {q,v} \right)}} \right)}_{x} = {p_{x} - {\frac{v_{x} - p_{x}}{v_{y}} \cdot {H\left( {{H\left( {p,v} \right)},{H\left( {q,v} \right)}} \right)}_{y}}}} \\{= {p_{x} - {\frac{v_{x} - p_{x}}{v_{y}} \cdot {- v_{y}}}}} \\{= v_{x}}\end{matrix}$

Thus, the vanishing point coordinates in the ERF are those of thevanishing point peak with the y component negated.

Alternatively to producing the second parameter space, the track-angleerror module 115 can be arranged to plot the lines represented by thepeaks in the first parameter space onto the ERF and determine theirintersection. In this example, the intersection would be the vanishingpoint.

The track-angle error module 115 can be arranged to calculate atrack-angle error (TKE) from the vanishing point. The ERF may bedistorted from the actual field by, for example, the type of sensor usedand the perspective of the sensor. For example, the sensor may bepositioned at a downward angle to provide a clearer perspective of thecrop rows and furrows. This position, however, may splay crop rows closeto the sensor and constrict them towards the horizon. Because the sensormay change its angle with respect to the horizon (view dip angle) overtime—for example, as it pitches up and down on uneven ground—the effectof the splay may be indeterminate prior to ascertaining the sensor'sperspective with respect to the horizon. However, the vanishing point islocated at the horizon and can provide the data necessary to adjust forthe vertical sensor angle. In an example, to calculate the TKE from thevanishing point, the track-angle error module 115 can be arranged tocalculate the view dip angle. As used herein, the view dip angle is thevertical declination of a sensor (e.g., an image capture device) fromhorizontal when an image of the field was taken. The track-angle errormodule 115 can be arranged to modify the ERF-track-angle error using theview dip angle to adjust for distortions between elements of the imageand corresponding elements of the field. In an example, the followingcan be used to adjust for the distortions:

A horizontal plane through the sensor's point of view and the vanishingpoint contains a line segment from the point of view to the image. Theacross-track component of that line segment is the x component of thevanishing point in the image. The along-track component is thesquare-root of the squares of the unit distance from the point of viewto the image and the y component of the vanishing point in the image.Therefore, the ratio of the y component to the root-sum-square is thenegative of the tangent of TKE:

${\tan \; {TKE}} = \frac{- v_{x}}{\sqrt{1 + v_{y}^{2}}}$

In an example, the track-angle error module 115 can be arranged tocommunicate the TKE to a steering module 130. The steering module 130can be arranged to use the TKE as a parameter to adjust approaches tothe target (e.g., crop row).

The cross-track distance module 120 can be arranged to identify a subsetof peaks in the first parameter space based on a line in the firstparameter space defined by the vanishing point peak. This can provideprotection against an erroneously identified peak that does notrepresent a line intersecting the vanishing point. One such example isillustrated in FIGS. 6 and 7 and described below. In an example, wherethere are no erroneously identified peaks, the subset of peaks is equalto the set of peaks in the first parameter space. Third and subsequentparameter spaces and be treated in a like manner to eliminateerroneously identified peaks in those parameter spaces.

The cross-track distance module 120 can be arranged to calculate a setof intermediate intercept differences between lines represented bymembers in the subset of peaks. These intercept differences can becalculated on an XTK line. The XTK line is any line intersecting thelines represented by the subset of peaks. In an example, the XTK line isparallel to the intercept axis parameter of the parameter space. Forexample, in the vertical SLIHT, the intercept axis is the x axis. Theline parallel to the x axis can be the axis itself, or another. In anexample, the line parallel to the intercept axis is the bottom of theERF in vertical SLIHT and the corresponding edge of the ERF (e.g., rightor left depending on rotation) in horizontal SLIHT. Generally, the moreperpendicular the XTK line is to the lines represented by the subset ofpeaks, the better the results become.

In an example, intermediate intercept differences can be calculated toreduce error. The calculation to reduce error can include determining adifference between every pair of members in the subset of peaks. Forexample, if the subset of peaks includes peak1, peak2, peak3, and peak4,the following differences (e.g., differences between corresponding linesintercepting the XTK line) can be calculated (peak1, peak2), (peak1,peak3), (peak1, peak4), (peak2, peak3), (peak2, peak4), and (peak3,peak4). The results from adjacent peaks can be binned together. Forexample, the pairs (peak1, peak3) and (peak2, peak4) can be binnedtogether. In an example, the differences in each bin can be averaged todetermine a single value for the bin.

The cross-track distance module 120 can be arranged to calculate asingle intercept difference in the ERF based on the set of intermediateintercept axis differences. The difference (or bin) that is the smallestof the intermediate intercept differences can be used to represent asingle spacing (e.g., between either crop rows or furrows). The largestdifference (or bin) can be divided by single spacing to determine aratio. This ratio can represent the number of elements encompassed bythe largest difference. In an example, for non-fractional elements, theratio can be rounded (e.g., quantized) to an integer. For example, ifthe ratio between the smallest and the largest difference is calculatedto 1:3.347, it can be rounded to 1:3, and the largest difference can beconsidered to encompass four crop rows. The largest difference can bedivided by the number of elements it encompasses to arrive at the singleintercept difference. By performing this division, error in theintermediate intercept differences is diffused across the elementsencompassed by the largest difference, resulting in reduced error forthe XTK calculation. Thus, the generally equal space between thefeatures (e.g., crop rows) can be determined and accuracy enhanced bycombining the various data points from the first parameter space peaks.In an example, the above can also be applied to the third and subsequentparameter spaces to, for example, determine the distance betweenfurrows.

The cross-track distance module 120 can be arranged to calculate the XTKbased on the single intercept axis difference. In an example, thecross-track distance module 120 can be arranged to calculate a cameraintercept on the XTK line for a line passing through both the vanishingpoint and a camera position (position line). The cross-track distancemodule 120 can be arranged to calculate a set of differences where eachmember of the set of differences is a difference between the cameraintercept and an intercept on the XTK line for lines represented by thesubset of peaks in the first parameter space. In an example, thecross-track distance module 120 can be arranged to apply a modulusoperation to each member of the set of differences using the singleintercept difference as a parameter to produce a set of results andcombine the members of the set of results. The modulus operation can usethe respective resultant differences and the single intercept axisdifference. In an example, the results can be averaged to determine theXTK.

An example modulus operation can include summing vectors representingeach peak in the subset of peaks in the first parameter space where eachvector's angle is the distance between the respective line's interceptand that of the camera intercept scaled 360° per the single interceptdifference. Thus, a second line away from the position line would bescaled 720°. The XTK can be calculated by summing the vectors. In anexample, a similar operation can be applied to the subset of peaks inthe third parameter space to produce respective vectors. To account forthe intermediate position of, for example, furrows represented in thethird parameter space between crop rows represented in the firstparameter space, an additional 180° can be applied to the 360° scalingdescribed above. The XTK is the angle of the vector sum.

In an example, the cross-track distance module can be arranged todetermine, from the first parameter space, a missing peak based on theline represented by the vanishing point peak and the single interceptdifference. For example, the subset of peaks should be spaced on thevanishing point peak line by the single intercept difference. If twopeaks are spaced by a multiple greater than one on the vanishing pointpeak line, one or more missing peaks can be inferred at intervals of thesingle intercept difference along the vanishing point peak line. In anexample, these missing peaks can be added to the subset of peaks in thefirst parameter space. In an example, after adding the missing peaks,the XTK can be the difference between the camera intercept and theclosest intercept of lines represented by the subset of peaks. Using themodulus operation or replacing missing peaks can provide continuity toAEQ navigation by inferring the XTK to the target even if the target ismomentarily interrupted (e.g., obscured, broken, etc.).

In an example, to calculate the XTK, the cross-track distance module 120can be arranged to apply a set of scaling operations. In an example,intermediate results can be scaled to the ERF. In an example, thescaling can include scaling from units of spacing (e.g., swath spacing)to units of distance. In an example, the scaling can include scaling bythe cosine of the TKE.

In an example, the cross-track distance module 120 can be arranged tocommunicate the XTK to the steering module 130. The steering module 130can be arranged to use the XTK as a parameter to adjust approaches tothe target (e.g., crop row).

FIGS. 2A-10 illustrate an example of the previously described featuresof the system 100. In this example, the feature sets are crop rowfeatures and furrow features.

FIG. 2A illustrates a top-down view of a vehicle 205 (e.g., AEQ) in afield. The field includes crop rows 210 and furrows 215. The line 220represents the center line of a crop row and the line 225 represents thecurrent orientation of the vehicle 205. The angle 230 is the TKE and thedistance 235 is the XTK. The vehicle 205 includes a sensor 240 arrangedto produce a source image.

FIG. 2B illustrates a profile view of the vehicle 205 in the field. Theline 245 represents the vertical orientation of the vehicle 205 withrespect to the horizon and the angle 250 is the current view dip angleof the sensor 240.

FIG. 3 illustrates an example of an ERF 300. The ERF 300 includes thehorizon 310, crop rows 210 (shaded), and furrows 215 (white). Alsoillustrated is a shading effect 305 represented by the diagonal stripes.As discussed above, the shading effect 305 can be removed via colormodeling (e.g., color normalization).

FIG. 4 illustrates an example of a Hough transform parameter space forcrop rows 400 (e.g., the first parameter space). For clarity theparameter space 400 is simplified to three values: dark, lightly shaded,and white. The dark values represent few pixels in the ERF 300 for theline represented by the parameter space position, the lightly shadedrepresents a medium number of pixels, and the white represents a highnumber of pixels. As described above, clusters of medium and highpositions can be merged to determine the peaks 405A-405E. The line 410illustrates that the peaks 405A-405E lie on a single line (and thusconverge).

FIG. 5 illustrates an example of determined crop row lines superimposedon the ERF 300 to produce an ERF 500. The crop row lines 505A-505Ecorrespond to the respective peaks 405A-405E. The sensor position 510relative to the ERF 500 is also shown.

FIG. 6 illustrates an example of a Hough transform parameter space forfurrows 600 (e.g., the third parameter space). The peaks 605A-605D aredetermined in the same manner described above with respect to FIG. 4.Also, the line 610 similarly demonstrates the convergence of linesrepresented by the peaks 605A-605D. The peak 605E illustrates anerroneously identified peak. Because the peak 605E does not lie on theline 610, it will not be considered in future XTK calculations.

FIG. 7 illustrates an example of determined furrow lines superimposed onthe ERF 300 to produce an ERF 700. The furrow lines 705A-705E correspondto the respective peaks 605A-605E. Note that the line 705E does notcorrespond to either a crop row 210 or a furrow 215, nor does itconverge with the other lines 705A-705D. Thus, the line 705E should beexcluded from future calculations.

FIG. 8 illustrates an example of a Hough transform parameter space 800of the Hough transform parameter spaces for crop rows 400 and furrows600. The peak 805 represents both the lines 410 and 610. The collectionof values 810 illustrates the result of the erroneous peak 605E from theparameter space 600.

FIG. 9 illustrates an example of determined crop row lines 505A-505E,furrow lines 705A-705D, and vanishing point 905 superimposed on the ERF300 to produce an ERF 900. From this data, the TKE and XTK can bedetermined as described above with respect to FIG. 1.

FIG. 10 illustrates an example of a graph 1000 for cross-track distancenormalization. Specifically, a rotational modulus operation isillustrated. The vectors 1005 represent the 360° scaled angulardifference of crop row intercepts to the camera intercept. The vector1010 is the sum of the vectors 1005. Similarly, the vectors 1015represent the scaled furrow row differences to the camera intercept,before being rotated by an additional 180°, and the vector 1020 is theirsum. As evident in the illustration, applying a 180° rotation to vectors1015, or to vector 1020, causes these vectors to generally align withthe vectors 1005 and vector 1020. In an example, all vectors 1005, 1010,1015, and 1020 can be summed to produce the XTK.

FIG. 11 illustrates an example of a method 1100 for row guidanceparameterization with Hough transform. One or more components describedabove can be used to perform one or more operations of the method 1100.Other capable hardware can be used to perform one or more operations ofthe method 1100.

At operation 1105, an ERF can be received. The ERF can include a set offeature sets. The set of feature sets can include at least one of a setof crop row features and a set of furrow features. In an example,receiving the ERF can include receiving a digital image of the field. Atransform can be applied to the digital image to produce the ERF. In anexample, the transform can include color modeling. In an example, thetransform can include downsampling. In an example, the downsampling caninclude image distortion correction. In an example, the transformincludes removing members of a feature set.

At operation 1110, a first parameter space can be produced by performinga SLIHT on members of a feature set in the set of feature sets. Thefirst parameter space can include a first slope parameter and a firstintercept parameter.

At operation 1115, peaks in the first parameter space can be identified.

At operation 1120, a second parameter space can be produced byperforming the SLIHT on the peaks. In an example, producing the secondparameter space can include producing a third parameter space byperforming the SLIHT on members of a second feature set in the set offeature sets. The feature set and the second feature set are differentmembers of the set of feature sets. Second peaks can be identified inthe third parameter space and the second parameter space can be adjustedwith the output of performing SLIHT on the second peaks.

At operation 1125, a vanishing point can be calculated based on avanishing point peak in the second parameter space. Alternatively, anintersection between lines represented by any plurality to all of thepeaks and the second peaks can be used to calculate the vanishing pointwithout producing the second parameter space and corresponding vanishingpoint peak.

At operation 1130, a TKE can be calculated from the vanishing point. Inan example, calculating the TKE from the vanishing point can includecalculating a view dip angle. The view dip angle is the verticaldeclination of a sensor (e.g., an image capture device) from horizontalwhen a source image of the field was taken. An ERF-track-angle error canbe modified using the view dip angle to adjust for distortions betweenelements of the source image and corresponding elements of the field.

FIG. 12 illustrates an example of a method 1200 for determining across-track distance. One or more components described above can be usedto perform one or more operations of the method 1200. Other capablehardware can be used to perform one or more operations of the method1200.

At operation 1205, a subset of peaks can be identified in the firstparameter space based on a line in the first parameter space defined bythe vanishing point peak.

At operation 1210, a set of intermediate intercept differences can becalculated from member pairs in the subset of peaks. The interceptdifferences can be calculated on an XTK line.

At operation 1215, a single intercept difference can be calculated inthe ERF based on the set of intermediate intercept axis differences.

At operation 1220, an XTK can be calculated based on the singleintercept axis difference. In an example, calculating the XTK caninclude applying a set of scaling operations. In an example, a cameraintercept on the XTK line for a line passing through both the vanishingpoint and a camera position can be calculated. A set of differences canbe calculated. Each member of the set of differences is a differencebetween the camera intercept and an intercept for a line represented bya member of the subset of peaks in the first parameter space. In anexample, a modulus operation can be applied to each member of the set ofdifferences using the single intercept difference as a parameter toproduce a set of results. The members of the set of results can then becombined.

FIG. 13 illustrates a block diagram of an example machine 1300 uponwhich any one or more of the techniques (e.g., methodologies) discussedherein may perform. In alternative embodiments, the machine 1300 mayoperate as a standalone device or may be connected (e.g., networked) toother machines. In a networked deployment, the machine 1300 may operatein the capacity of a server machine, a client machine, or both inserver-client network environments. In an example, the machine 1300 mayact as a peer machine in peer-to-peer (P2P) (or other distributed)network environment. The machine 1300 may be a personal computer (PC), atablet PC, a set-top box (STB), a personal digital assistant (PDA), amobile telephone, a web appliance, a network router, switch or bridge,or any machine capable of executing instructions (sequential orotherwise) that specify actions to be taken by that machine. Further,while only a single machine is illustrated, the term “machine” shallalso be taken to include any collection of machines that individually orjointly execute a set (or multiple sets) of instructions to perform anyone or more of the methodologies discussed herein, such as cloudcomputing, software as a service (SaaS), other computer clusterconfigurations.

Examples, as described herein, may include, or may operate on, logic ora number of components, modules, or mechanisms. Modules are tangibleentities (e.g., hardware) capable of performing specified operations andmay be configured or arranged in a certain manner. In an example,circuits may be arranged (e.g., internally or with respect to externalentities such as other circuits) in a specified manner as a module. Inan example, the whole or part of one or more computer systems (e.g., astandalone, client or server computer system) or one or more hardwareprocessors may be configured by firmware or software (e.g.,instructions, an application portion, or an application) as a modulethat operates to perform specified operations. In an example, thesoftware may reside on a machine readable medium. In an example, thesoftware, when executed by the underlying hardware of the module, causesthe hardware to perform the specified operations.

Accordingly, the term “module” is understood to encompass a tangibleentity, be that an entity that is physically constructed, specificallyconfigured (e.g., hardwired), or temporarily (e.g., transitorily)configured (e.g., programmed) to operate in a specified manner or toperform part or all of any operation described herein. Consideringexamples in which modules are temporarily configured, each of themodules need not be instantiated at any one moment in time. For example,where the modules comprise a general-purpose hardware processorconfigured using software, the general-purpose hardware processor may beconfigured as respective different modules at different times. Softwaremay accordingly configure a hardware processor, for example, toconstitute a particular module at one instance of time and to constitutea different module at a different instance of time.

Machine (e.g., computer system) 1300 may include a hardware processor1302 (e.g., a central processing unit (CPU), a graphics processing unit(GPU), a hardware processor core, or any combination thereof), a mainmemory 1304 and a static memory 1306, some or all of which maycommunicate with each other via an interlink (e.g., bus) 1308. Themachine 1300 may further include a display unit 1310, an alphanumericinput device 1312 (e.g., a keyboard), and a user interface (UI)navigation device 1314 (e.g., a mouse). In an example, the display unit1310, input device 1312 and UI navigation device 1314 may be a touchscreen display. The machine 1300 may additionally include a storagedevice (e.g., drive unit) 1316, a signal generation device 1318 (e.g., aspeaker), a network interface device 1320, and one or more sensors 1321,such as a global positioning system (GPS) sensor, compass,accelerometer, or other sensor. The machine 1300 may include an outputcontroller 1328, such as a serial (e.g., universal serial bus (USB),parallel, or other wired or wireless (e.g., infrared (IR), near fieldcommunication (NFC), etc.) connection to communicate or control one ormore peripheral devices (e.g., a printer, card reader, etc.).

The storage device 1316 may include a machine readable medium 1322 onwhich is stored one or more sets of data structures or instructions 1324(e.g., software) embodying or utilized by any one or more of thetechniques or functions described herein. The instructions 1324 may alsoreside, completely or at least partially, within the main memory 1304,within static memory 1306, or within the hardware processor 1302 duringexecution thereof by the machine 1300. In an example, one or anycombination of the hardware processor 1302, the main memory 1304, thestatic memory 1306, or the storage device 1316 may constitute machinereadable media.

While the machine readable medium 1322 is illustrated as a singlemedium, the term “machine readable medium” may include a single mediumor multiple media (e.g., a centralized or distributed database, and/orassociated caches and servers) configured to store the one or moreinstructions 1324.

The term “machine readable medium” may include any medium that iscapable of storing, encoding, or carrying instructions for execution bythe machine 1300 and that cause the machine 1300 to perform any one ormore of the techniques of the present disclosure, or that is capable ofstoring, encoding or carrying data structures used by or associated withsuch instructions. Non-limiting machine readable medium examples mayinclude solid-state memories, and optical and magnetic media. In anexample, a massed machine readable medium comprises a machine readablemedium with a plurality of particles having resting mass. Specificexamples of massed machine readable media may include: non-volatilememory, such as semiconductor memory devices (e.g., ElectricallyProgrammable Read-Only Memory (EPROM), Electrically ErasableProgrammable Read-Only Memory (EEPROM)) and flash memory devices;magnetic disks, such as internal hard disks and removable disks;magneto-optical disks; and CD-ROM and DVD-ROM disks.

The instructions 1324 may further be transmitted or received over acommunications network 1326 using a transmission medium via the networkinterface device 1320 utilizing any one of a number of transferprotocols (e.g., frame relay, internet protocol (IP), transmissioncontrol protocol (TCP), user datagram protocol (UDP), hypertext transferprotocol (HTTP), etc.). Example communication networks may include alocal area network (LAN), a wide area network (WAN), a packet datanetwork (e.g., the Internet), mobile telephone networks (e.g., cellularnetworks), Plain Old Telephone (POTS) networks, and wireless datanetworks (e.g., Institute of Electrical and Electronics Engineers (IEEE)802.11 family of standards known as Wi-Fi®, IEEE 802.16 family ofstandards known as WiMax®), IEEE 802.15.4 family of standards,peer-to-peer (P2P) networks, among others. In an example, the networkinterface device 1320 may include one or more physical jacks (e.g.,Ethernet, coaxial, or phone jacks) or one or more antennas to connect tothe communications network 1326. In an example, the network interfacedevice 1320 may include a plurality of antennas to wirelesslycommunicate using at least one of single-input multiple-output (SIMO),multiple-input multiple-output (MIMO), or multiple-input single-output(MISO) techniques. The term “transmission medium” shall be taken toinclude any intangible medium that is capable of storing, encoding orcarrying instructions for execution by the machine 1300, and includesdigital or analog communications signals or other intangible medium tofacilitate communication of such software.

ADDITIONAL NOTES & EXAMPLES

Example 1 can include subject matter (such as a method, means forperforming acts, or machine readable medium including instructions that,when performed by a machine cause the machine to performs acts)comprising receiving an electronic representation of a field (ERF)including a set of feature sets—the set of feature sets including atleast one of a set of crop row features and a set of furrow features,producing a first parameter space by performing a slope-intercept Houghtransform (SLIHT) on members of a feature set in the set of featuresets—the first parameter space including a first slope parameter and afirst intercept parameter, identifying peaks in the first parameterspace, producing a second parameter space by performing the SLIHT on thepeaks, calculating a vanishing point based on a vanishing point peak inthe second parameter space, and calculating a track-angle error (TKE)from the vanishing point.

In Example 2, the subject matter of Example 1 can optionally includewherein producing the second parameter space includes producing a thirdparameter space by performing the SLIHT on members of a second featureset in the set of feature sets—the feature set and the second featureset being different members of the set of feature sets, identifyingsecond peaks in the third parameter space, and adjusting the secondparameter space with the output of performing SLIHT on the second peaks.

In Example 3, the subject matter of any one or more of Examples 1-2 canoptionally include, wherein receiving the ERF includes receiving adigital image of the field, and applying a transform to the digitalimage to produce the ERF.

In Example 4, the subject matter of Example 3 can optionally include,wherein the transform includes color modeling.

In Example 5, the subject matter of any one or more of Examples 3-4 canoptionally include, wherein the transform includes downsampling.

In Example 6, the subject matter of Example 5 can optionally include,wherein the downsampling includes image distortion correction.

In Example 7, the subject matter of any one or more of Examples 3-6 canoptionally include, wherein the transform includes removing members of afeature set.

In Example 8, the subject matter of any one or more of Examples 1-7 canoptionally include, wherein calculating the TKE from the vanishing pointincludes calculating a view dip angle, the view dip angle being thevertical declination of an image capture device from horizontal when animage of the field was taken, the ERF being derived from the image ofthe field, and modifying an ERF-track-angle error using the view dipangle to adjust for distortions between elements of the image andcorresponding elements of the field.

In Example 9, the subject matter of any one or more of Examples 1-8 canoptionally include, identifying a subset of peaks in the first parameterspace based on a line in the first parameter space defined by thevanishing point peak, calculating a set of intermediate interceptdifferences from member pairs in the subset of peaks, the interceptdifferences calculated on an XTK line, calculating a single interceptdifference in the ERF based on the set of intermediate interceptdifferences, and calculating a cross-track distance (XTK) based on thesingle intercept difference.

In Example 10, the subject matter of Example 9 can optionally include,wherein calculating the XTK includes applying a set of scalingoperations.

In Example 11, the subject matter of any one or more of Examples 9-10can optionally include, wherein calculating the XTK includes calculatinga camera intercept on the XTK line for a line passing through both thevanishing point and a camera position, and calculating a set ofdifferences, each member of the set of differences being a differencebetween the camera intercept and an intercept for a line represented bya member of the subset of peaks in the first parameter space, applying amodulus operation to each member of the set of differences using thesingle intercept difference as a parameter to produce a set of results,and combining the members of the set of results.

Example 12 can include, or may optionally be combined with the subjectmatter of any one of Examples 1-11 to include subject matter (such as amodule, device, apparatus row guidance parameterization with Houghtransform) comprising a scene module arranged to receive an electronicrepresentation of a field (ERF) including a set of feature sets—the setof feature sets including at least one of a set of crop row features anda set of furrow features. The subject matter can also comprise atransform module arranged to produce a first parameter space byperforming a slope-intercept Hough transform (SLIHT) on members of afeature set in the set of feature sets—the first parameter spaceincluding a first slope parameter and a first intercept parameter,identify peaks in the first parameter space, and produce a secondparameter space by performing the SLIHT on the peaks. The subject mattercan also comprise a track-angle error module arranged to calculate avanishing point based on a vanishing point peak in the second parameterspace, and calculate a track-angle error (TKE) from the vanishing point.

In Example 13, the subject matter of Example 12 can optionally include,wherein to produce the second parameter space includes the transformmodule arranged to produce a third parameter space by performing theSLIHT on members of a second feature set in the set of feature sets—thefeature set and the second feature set being different members of theset of feature sets, identify second peaks in the third parameter space,and adjust the second parameter space with the output of performingSLIHT on the second peaks.

In Example 14, the subject matter of any one or more of Examples 12-13can optionally include, wherein to receive the ERF includes the scenemodule arranged to receive a digital image of the field, and apply atransform to the digital image to produce the ERF.

In Example 15, the subject matter of Example 14 can optionally include,wherein the transform includes color modeling.

In Example 16, the subject matter of any one or more of Examples 14-15can optionally include, wherein the transform includes downsampling.

In Example 17, the subject matter of Example 16 can optionally include,wherein the downsampling includes image distortion correction.

In Example 18, the subject matter of any one or more of Examples 14-17can optionally include, wherein the transform includes removing membersof a feature set.

In Example 19, the subject matter of any one or more of Examples 12-17can optionally include, wherein to calculate the TKE from the vanishingpoint includes the track-angle error module arranged to calculate a viewdip angle, the view dip angle being the vertical declination of an imagecapture device from horizontal when an image of the field was taken—theERF being derived from the image of the field, and modify anERF-track-angle error using the view dip angle to adjust for distortionsbetween elements of the image and corresponding elements of the field.

In Example 20, the subject matter of any one or more of Examples 12-19can optionally include a cross-track distance module arranged toidentify a subset of peaks in the first parameter space based on a linein the first parameter space defined by the vanishing point peak,calculate a set of intermediate intercept differences from member pairsin the subset of peaks—the intercept differences calculated on an XTKline, calculate a single intercept difference in the ERF based on theset of intermediate intercept differences, and calculate a cross-trackdistance (XTK) based on the single intercept difference.

In Example 21, the subject matter of Example 20 can optionally include,wherein to calculate the XTK includes the cross-track distance modulearranged to apply a set of scaling operations.

In Example 22, the subject matter of any one or more of Examples 20-21can optionally include, wherein to calculate the XTK includes thecross-track distance module arranged to calculate a camera intercept onthe XTK line for a line passing through both the vanishing point and acamera position, and calculate a set of differences, each member of theset of differences being a difference between the camera intercept andan intercept for a line represented by a member of the subset of peaksin the first parameter space, apply a modulus operation to each memberof the set of differences using the single intercept difference as aparameter to produce a set of results, and combine the members of theset of results.

The above detailed description includes references to the accompanyingdrawings, which form a part of the detailed description. The drawingsshow, by way of illustration, specific embodiments that may bepracticed. These embodiments are also referred to herein as “examples.”Such examples can include elements in addition to those shown ordescribed. However, the present inventors also contemplate examples inwhich only those elements shown or described are provided. Moreover, thepresent inventors also contemplate examples using any combination orpermutation of those elements shown or described (or one or more aspectsthereof), either with respect to a particular example (or one or moreaspects thereof), or with respect to other examples (or one or moreaspects thereof) shown or described herein.

All publications, patents, and patent documents referred to in thisdocument are incorporated by reference herein in their entirety, asthough individually incorporated by reference. In the event ofinconsistent usages between this document and those documents soincorporated by reference, the usage in the incorporated reference(s)should be considered supplementary to that of this document; forirreconcilable inconsistencies, the usage in this document controls.

In this document, the terms “a” or “an” are used, as is common in patentdocuments, to include one or more than one, independent of any otherinstances or usages of “at least one” or “one or more.” In thisdocument, the term “or” is used to refer to a nonexclusive or, such that“A or B” includes “A but not B,” “B but not A,” and “A and B,” unlessotherwise indicated. In the appended claims, the terms “including” and“in which” are used as the plain-English equivalents of the respectiveterms “comprising” and “wherein.” Also, in the following claims, theterms “including” and “comprising” are open-ended, that is, a system,device, article, or process that includes elements in addition to thoselisted after such a term in a claim are still deemed to fall within thescope of that claim. Moreover, in the following claims, the terms“first,” “second,” and “third,” etc. are used merely as labels, and arenot intended to impose numerical requirements on their objects.

The above description is intended to be illustrative, and notrestrictive. For example, the above-described examples (or one or moreaspects thereof) may be used in combination with each other. Otherembodiments can be used, such as by one of ordinary skill in the artupon reviewing the above description. The Abstract is to allow thereader to quickly ascertain the nature of the technical disclosure, forexample, to comply with 37 C.F.R. §1.72(b) in the United States ofAmerica. It is submitted with the understanding that it will not be usedto interpret or limit the scope or meaning of the claims. Also, in theabove Detailed Description, various features may be grouped together tostreamline the disclosure. This should not be interpreted as intendingthat an unclaimed disclosed feature is essential to any claim. Rather,inventive subject matter may lie in less than all features of aparticular disclosed embodiment. Thus, the following claims are herebyincorporated into the Detailed Description, with each claim standing onits own as a separate embodiment. The scope of the embodiments should bedetermined with reference to the appended claims, along with the fullscope of equivalents to which such claims are entitled.

What is claimed is:
 1. A massed machine-readable medium (MMRM) includinginstructions that, when executed by a machine, cause the machine toperform operations comprising: receiving an electronic representation ofa field (ERF) including a set of feature sets, the set of feature setsincluding at least one of a set of crop row features and a set of furrowfeatures; producing a first parameter space by performing aslope-intercept Hough transform (SLIHT) on members of a feature set inthe set of feature sets, the first parameter space including a firstslope parameter and a first intercept parameter; identifying peaks inthe first parameter space; producing a second parameter space byperforming the SLIHT on the peaks; calculating a vanishing point basedon a vanishing point peak in the second parameter space; and calculatinga track-angle error (TKE) from the vanishing point.
 2. The MMRM of claim1, wherein producing the second parameter space includes: producing athird parameter space by performing the SLIHT on members of a secondfeature set in the set of feature sets, the feature set and the secondfeature set being different members of the set of feature sets;identifying second peaks in the third parameter space; and adjusting thesecond parameter space with a result from performing SLIHT on the secondpeaks.
 3. The MMRM of claim 1, wherein receiving the ERF includes:receiving a digital image of the field; and applying a transform to thedigital image to produce the ERF.
 4. The MMRM of claim 3, wherein thetransform includes color modeling.
 5. The MMRM of claim 3, wherein thetransform includes downsampling.
 6. The MMRM of claim 5, wherein thedownsampling includes image distortion correction.
 7. The MMRM of claim3, wherein the transform includes removing members of the feature set.8. The MMRM of claim 1, wherein calculating the TKE from the vanishingpoint includes: calculating a view dip angle, the view dip angle being avertical declination of an image capture device from horizontal when animage of the field was taken, the ERF being derived from the image ofthe field; and modifying an ERF-track-angle error using the view dipangle to adjust for distortions between elements of the image andcorresponding elements of the field.
 9. The MMRM of claim 1, wherein theinstructions, when executed, cause the machine to perform operationscomprising: identifying a subset of peaks in the first parameter spacebased on a line in the first parameter space defined by the vanishingpoint peak; calculating a set of intermediate intercept differences frommember pairs in the subset of peaks, the intercept differencescalculated on an XTK line; calculating a single intercept difference inthe ERF based on the set of intermediate intercept differences; andcalculating a cross-track distance (XTK) based on the single interceptdifference.
 10. The MMRM of claim 9, wherein calculating the XTKincludes applying a set of scaling operations.
 11. The MMRM of claim 9,wherein calculating the XTK includes: calculating a camera intercept onthe XTK line for a line passing through both the vanishing point and acamera position; and calculating a set of differences, each member ofthe set of differences being a difference between the camera interceptand an intercept for a line represented by a member of the subset ofpeaks in the first parameter space; applying a modulus operation to eachmember of the set of differences using the single intercept differenceas a parameter to produce a set of results; and combining the members ofthe set of results.
 12. A system comprising: a scene module arranged toreceive an electronic representation of a field (ERF) including a set offeature sets, the set of feature sets including at least one of a set ofcrop row features and a set of furrow features; a transform modulearranged to: produce a first parameter space by performing aslope-intercept Hough transform (SLIHT) on members of a feature set inthe set of feature sets, the first parameter space including a firstslope parameter and a first intercept parameter; identify peaks in thefirst parameter space; and produce a second parameter space byperforming the SLIHT on the peaks; and a track-angle error modulearranged to: calculate a vanishing point based on a vanishing point peakin the second parameter space; and calculate a track-angle error (TKE)from the vanishing point.
 13. The system of claim 12, wherein to producethe second parameter space includes the transform module arranged to:produce a third parameter space by performing the SLIHT on members of asecond feature set in the set of feature sets, the feature set and thesecond feature set being different members of the set of feature sets;identify second peaks in the third parameter space; and adjust thesecond parameter space with a result from performing SLIHT on the secondpeaks.
 14. The system of claim 12, wherein to receive the ERF includesthe scene module arranged to: receive a digital image of the field; andapply a transform to the digital image to produce the ERF.
 15. Thesystem of claim 14, wherein the transform includes color modeling. 16.The system of claim 14, wherein the transform includes downsampling. 17.The system of claim 16, wherein the downsampling includes imagedistortion correction.
 18. The system of claim 14, wherein the transformincludes removing members of a feature set.
 19. The system of claim 12,wherein to calculate the TKE from the vanishing point includes thetrack-angle error module arranged to: calculate a view dip angle, theview dip angle being a vertical declination of an image capture devicefrom horizontal when an image of the field was taken, the ERF beingderived from the image of the field; and modify an ERF-track-angle errorusing the view dip angle to adjust for distortions between elements ofthe image and corresponding elements of the field.
 20. The system ofclaim 12 comprising a cross-track distance module arranged to: identifya subset of peaks in the first parameter space based on a line in thefirst parameter space defined by the vanishing point peak; calculate aset of intermediate intercept differences from member pairs in thesubset of peaks, the intercept differences calculated on an XTK line;calculate a single intercept difference in the ERF based on the set ofintermediate intercept differences; and calculate a cross-track distance(XTK) based on the single intercept difference.
 21. The system of claim20, wherein to calculate the XTK includes the cross-track distancemodule arranged to apply a set of scaling operations.
 22. The system ofclaim 20, wherein to calculate the XTK includes the cross-track distancemodule arranged to: calculate a camera intercept on the XTK line for aline passing through both the vanishing point and a camera position;calculate a set of differences, each member of the set of differencesbeing a difference between the camera intercept and an intercept for aline represented by a member of the subset of peaks in the firstparameter space; apply a modulus operation to each member of the set ofdifferences using the single intercept difference as a parameter toproduce a set of results; and combine members of the set of results. 23.A method comprising: receiving an electronic representation of a field(ERF) including a set of feature sets, the set of feature sets includingat least one of a set of crop row features and a set of furrow features;producing a first parameter space by performing a slope-intercept Houghtransform (SLIHT) on members of a feature set in the set of featuresets, the first parameter space including a first slope parameter and afirst intercept parameter; identifying peaks in the first parameterspace; producing a second parameter space by performing the SLIHT on thepeaks; calculating a vanishing point based on a vanishing point peak inthe second parameter space; and calculating a track-angle error (TKE)from the vanishing point.
 24. The method of claim 23, wherein producingthe second parameter space includes: producing a third parameter spaceby performing the SLIHT on members of a second feature set in the set offeature sets, the feature set and the second feature set being differentmembers of the set of feature sets; identifying second peaks in thethird parameter space; and adjusting the second parameter space with aresult from performing SLIHT on the second peaks.
 25. The method ofclaim 23, wherein receiving the ERF includes: receiving a digital imageof the field; and applying a transform to the digital image to producethe ERF.
 26. The method of claim 25, wherein the transform includescolor modeling.
 27. The method of claim 25, wherein the transformincludes downsampling.
 28. The method of claim 27, wherein thedownsampling includes image distortion correction.
 29. The method ofclaim 25, wherein the transform includes removing members of the featureset.
 30. The method of claim 23, wherein calculating the TKE from thevanishing point includes: calculating a view dip angle, the view dipangle being a vertical declination of an image capture device fromhorizontal when an image of the field was taken, the ERF being derivedfrom the image of the field; and modifying an ERF-track-angle errorusing the view dip angle to adjust for distortions between elements ofthe image and corresponding elements of the field.
 31. The method ofclaim 23 comprising: identifying a subset of peaks in the firstparameter space based on a line in the first parameter space defined bythe vanishing point peak; calculating a set of intermediate interceptdifferences from member pairs in the subset of peaks, the interceptdifferences calculated on an XTK line; calculating a single interceptdifference in the ERF based on the set of intermediate interceptdifferences; and calculating a cross-track distance (XTK) based on thesingle intercept difference.
 32. The method of claim 31, whereincalculating the XTK includes applying a set of scaling operations. 33.The method of claim 31, wherein calculating the XTK includes:calculating a camera intercept on the XTK line for a line passingthrough both the vanishing point and a camera position; calculating aset of differences, each member of the set of differences being adifference between the camera intercept and an intercept for a linerepresented by a member of the subset of peaks in the first parameterspace; applying a modulus operation to each member of the set ofdifferences using the single intercept difference as a parameter toproduce a set of results; and combining the members of the set ofresults.